Part III

Deep Learning Research

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This part of the book describes the more ambitious and advanced approaches

to deep learning, currently pursued by the research community.

In the previous parts of the book, we have shown how to solve supervised

learning problems—how to learn to map one vector to another, given enough

examples of the mapping.

Not all problems we might want to solve fall into this category. We may

wish to generate new examples, or determine how likely some point is, or handle

missing values and take advantage of a large set of unlabeled examples or examples

from related tasks. A shortcoming of the current state of the art for industrial

applications is that our learning algorithms require large amounts of supervised

data to achieve good accuracy. In this part of the book, we discuss some of

the speculative approaches to reducing the amount of labeled data necessary

for existing models to work well and be applicable across a broader range of

tasks. Accomplishing these goals usually requires some form of unsupervised or

semi-supervised learning.

Many deep learning algorithms have been designed to tackle unsupervised

learning problems, but none have truly solved the problem in the same way that

deep learning has largely solved the supervised learning problem for a wide variety of

tasks. In this part of the book, we describe the existing approaches to unsupervised

learning and some of the popular thought about how we can make progress in this

ﬁeld.

A central cause of the diﬃculties with unsupervised learning is the high di-

mensionality of the random variables being modeled. This brings two distinct

challenges: a statistical challenge and a computational challenge. The statistical

challenge regards generalization: the number of conﬁgurations we may want to

distinguish can grow exponentially with the number of dimensions of interest, and

this quickly becomes much larger than the number of examples one can possibly

have (or use with bounded computational resources). The computational challenge

associated with high-dimensional distributions arises because many algorithms for

learning or using a trained model (especially those based on estimating an explicit

probability function) involve intractable computations that grow exponentially

with the number of dimensions.

With probabilistic models, this computational challenge arises from the need to

perform intractable inference or simply from the need to normalize the distribution.

•

Intractable inference: inference is discussed mostly in chapter 19. It regards

the question of guessing the probable values of some variables

a

, given other

variables

b

, with respect to a model that captures the joint distribution over

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a

,

b

and

c

. In order to even compute such conditional probabilities one needs

to sum over the values of the variables

c

, as well as compute a normalization

constant which sums over the values of a and c.

•

Intractable normalization constants (the partition function): the partition

function is discussed mostly in chapter 18. Normalizing constants of proba-

bility functions come up in inference (above) as well as in learning. Many

probabilistic models involve such a normalizing constant. Unfortunately,

learning such a model often requires computing the gradient of the loga-

rithm of the partition function with respect to the model parameters. That

computation is generally as intractable as computing the partition function

itself. Monte Carlo Markov chain (MCMC) methods (chapter 17) are of-

ten used to deal with the partition function (computing it or its gradient).

Unfortunately, MCMC methods suﬀer when the modes of the model distribu-

tion are numerous and well-separated, especially in high-dimensional spaces

(section 17.5).

One way to confront these intractable computations is to approximate them,

and many approaches have been proposed as discussed in this third part of the

book. Another interesting way, also discussed here, would be to avoid these

intractable computations altogether by design, and methods that do not require

such computations are thus very appealing. Several generative models have been

proposed in recent years, with that motivation. A wide variety of contemporary

approaches to generative modeling are discussed in chapter 20.

Part III is the most important for a researcher—someone who wants to un-

derstand the breadth of perspectives that have been brought to the ﬁeld of deep

learning, and push the ﬁeld forward towards true artiﬁcial intelligence.

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